Figure 3

Diagrammatic expansions. Diagrammatic expansions of the renormalized propagators of the upper field \({\tilde{\Delta }}_{2}^{(1)}(k,\omega )\) (thick double-line) & the lower field \({\tilde{\Delta }}_{1}^{(1)}(k,\omega )\) (thick single-line) represented by the sum of free propagators of the upper field \({\tilde{\Delta }}_{2}^{(0)}(k,\omega )\) (thin double-line) & the lower field \({\tilde{\Delta }}_{1}^{(0)}(k,\omega )\) (thin single-line). The black dot “●” is the effective coupling v_P (Eq. (12)).